On some invariants in numerical semigroups and estimations of the order bound

We study suitable parameters and relations in a numerical semigroup S. When S is the Weierstrass semigroup at a rational point P of a projective curve C, we evaluate the Feng-Rao order bound of the associated family of Goppa codes. Further we conjecture that the order bound is always greater than a fixed value easily deduced from the parameters of the semigroup: we also prove this inequality in several cases

Exact dimensionality and projections of random self-similar measures and sets

We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact-dimensional, generalizing Feng and Hu's result \cite{FeHu09} for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic self-similar measures \cite{HoSh12} to these random measures without requiring any separation conditions on the underlying sets. We give applications to self-similar sets and fractal percolation, including new results on projections, $C^1$-images and distance sets.Comment: 25 page

Neutron-Diffraction Measurements of an Antiferromagnetic Semiconducting Phase in the Vicinity of the High-Temperature Superconducting State of Kx_xFe2−y_{2-y}Se2_2

The recently discovered K-Fe-Se high temperature superconductor has caused heated debate regarding the nature of its parent compound. Transport, angle-resolved photoemission spectroscopy, and STM measurements have suggested that its parent compound could be insulating, semiconducting or even metallic [M. H. Fang, H.-D. Wang, C.-H. Dong, Z.-J. Li, C.-M. Feng, J. Chen, and H. Q. Yuan, Europhys. Lett. 94, 27009 (2011); F. Chen et al. Phys. Rev. X 1, 021020 (2011); and W. Li et al.,Phys. Rev. Lett. 109, 057003 (2012)]. Because the magnetic ground states associated with these different phases have not yet been identified and the relationship between magnetism and superconductivity is not fully understood, the real parent compound of this system remains elusive. Here, we report neutron-diffraction experiments that reveal a semiconducting antiferromagnetic (AFM) phase with rhombus iron vacancy order. The magnetic order of the semiconducting phase is the same as the stripe AFM order of the iron pnictide parent compounds. Moreover, while the root5*root5 block AFM phase coexists with superconductivity, the stripe AFM order is suppressed by it. This leads us to conjecture that the new semiconducting magnetic ordered phase is the true parent phase of this superconductor.Comment: 1 table, 4 figures,5 page

Probiotic<i> Bacillus subtilis</i> protects against α-synuclein aggregation in <i>C. elegans</i>

How the gut microbiome affects Parkinson's disease remains unclear. Goya et al. show that the probiotic B. subtilis strain PXN21 inhibits and clears α-synuclein aggregation in a C. elegans model. The bacterium acts via metabolites and biofilm formation to activate protective pathways in the host, including DAF-16/FOXO and sphingolipid metabolism.Fil: Goya, María Eugenia. University of Edinburgh; Reino UnidoFil: Xue, Feng. University of Edinburgh; Reino UnidoFil: Sampedro Torres Quevedo, Cristina. University of Edinburgh; Reino UnidoFil: Arnaouteli, Sofia. University Of Dundee; Reino UnidoFil: Riquelme Dominguez, Lourdes. University of Edinburgh; Reino UnidoFil: Romanowski, Andrés. University of Edinburgh; Reino Unido. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquímicas de Buenos Aires. Fundación Instituto Leloir. Instituto de Investigaciones Bioquímicas de Buenos Aires; ArgentinaFil: Brydon, Jack. University of Edinburgh; Reino UnidoFil: Ball, Kathryn L.. University of Edinburgh; Reino UnidoFil: Stanley-Wall, Nicola R.. University Of Dundee; Reino UnidoFil: Doitsidou, Maria. University of Edinburgh; Reino Unid